The test positive rate is the fraction of all COVID-19 tests that are positive.
\[ \large \begin{equation} r_v = \frac{n_p}{n_p+n_n} \end{equation} \]
\(\large Where: r_v \hspace{1mm} is \hspace{1mm} the \hspace{1mm} test \hspace{1mm} positive \hspace{1mm} rate\)
\(\large \hspace{20mm}n_p \hspace{1mm} is \hspace{1mm} the \hspace{1mm} number \hspace{1mm} of \hspace{1mm} positive \hspace{1mm} tests\)
\(\large \hspace{20mm}n_n \hspace{1mm} is \hspace{1mm} the \hspace{1mm} number \hspace{1mm} of \hspace{1mm} negative \hspace{1mm} tests\)
According to Johns Hopkins:
The percent positive will be high if the number of positive tests is too high, or if the number of total tests is too low. A higher percent positive suggests higher transmission and that there are likely more people with coronavirus in the community who haven’t been tested yet.
The percent positive is a critical measure because it gives us an indication how widespread infection is in the area where the testing is occurring—and whether levels of testing are keeping up with levels of disease transmission.
A high percent positive means that more testing should probably be done—and it suggests that it is not a good time to relax restrictions aimed at reducing coronavirus transmission. Because a high percentage of positive tests suggests high coronavirus infection rates (due to high transmission in the community), a high percent positive can indicate it may be a good time to add restrictions to slow the spread of disease.
The higher the percent positive is, the more concerning it is. As a rule of thumb, however, one threshold for the percent positive being “too high” is 5%.
The confirmed daily cases curve that is often reported can be misleading. It fails to account for the number of daily tests and thus skews the daily cases towards points in time when more tests were done. Testing has increased significantly since the start of the pandemic and thus it must be accounted for when trying to estimate the actual number of cases over time. For example, in the U.S. in mid March 2020 only about 10,000 tests were done per day, but by the end of October 2020 1 million tests were being done each day.
One way to estimate the actual number of cases in a way that accounts for testing is to normalize the number of confirmed positive tests by the test positive rate and multiply by by a constant, referred to here as the antibody constant.
Almost all references to testing on this page are for viral PCR tests. The one exception is the antibody seroprevalence which is based on serology tests that look for antibodies which can show prior exposure to COVID-19. Johns Hopkins has more details on viral PCR and antibody serological tests.
The test positive rate is used to correct the shape of the cases curve over time as the number of tests change, and the antibody constant is used to calibrate the magnitude of the cases curve to a known antibody seroprevalence survey.
\[ \large \begin{equation} n_a = k_s \times n_p \times r_v = k_s \times n_p \times \frac{n_p}{n_p+n_n} = k_s \times \frac{{n_p}^2}{n_p+n_n} \end{equation} \]
\(\large Where:n_a \hspace{1mm} is \hspace{1mm} the \hspace{1mm} actual \hspace{1mm} number \hspace{1mm} of \hspace{1mm} cases\)
\(\large \hspace{20mm}k_s \hspace{1mm} is \hspace{1mm} the \hspace{1mm} antibody \hspace{1mm} constant\)
\(\large \hspace{20mm}n_p \hspace{1mm} is \hspace{1mm} the \hspace{1mm} number \hspace{1mm} of \hspace{1mm} positive \hspace{1mm} tests\)
\(\large \hspace{20mm}r_v \hspace{1mm} is \hspace{1mm} the \hspace{1mm} test \hspace{1mm} positive \hspace{1mm} rate\)
\(\large \hspace{20mm}n_n \hspace{1mm} is \hspace{1mm} the \hspace{1mm} number \hspace{1mm} of \hspace{1mm} negative \hspace{1mm} tests\)
The antibody constant is found by solving for ks in the equation below. The antibody seroprevalence rs is from the CDC’s Nationwide Commercial Laboratory Seroprevalence Survey that was done during the first two weeks of August 2020.
\[ \large \begin{equation} r_s = \frac{k_s}{N} \times \frac{{n_p}^2}{n_p+n_n} \end{equation} \] \(\large Where:r_s \hspace{1mm} is \hspace{1mm} the \hspace{1mm} antibody \hspace{1mm} seroprevalence\)
\(\large \hspace{20mm}N \hspace{1mm} is \hspace{1mm} the \hspace{1mm} total \hspace{1mm} population\)